Broadcasting expressions don't work with `deepcopied` ClimaCore spaces

[Sbozzolo]

Given that

using ClimaCore.CommonSpaces
space = CubedSphereSpace(;
           radius = 10,
           n_quad_points = 4,
           h_elem = 10,
       )

cop_space = deepcopy(space)

space == cop_space
# false (as expected, that's the point of deepcopying)

Fields defined on space and cannot be mixed with Fields defined on cop_space, even if the two spaces are identical (but not the same)

[charleskawczynski]

IIRC, this was a design choice / feature, and there are issues (some may be closed) that reference this behavior. I think the ClimaCore.Utilities.Cache.OBJECT_CACHE is related, as that basically allows us to compare whether spaces are safe to broadcast with. You should be able to track it down, and related issues, via git blame.

IMO, we could have done things a bit differently that would have allowed broadcasting with different pointers. That approach would have been a bit more work, though.

[Sbozzolo]

Yes, I opened this issue mostly to have it on record and for other people to be aware of it. It took me a few hours of debugging to understand why I was getting a "Spaces are not compatible".